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Each time you visit the NRICH site there will be some activities which are 'live'. This means we are inviting students to send us solutions, and we will publish a selection of them, along with each student's name and their school, a few weeks later. If you'd like to know more about what we're looking for, read this short article.
The last day for sending in solutions to these live problems is Monday 27 November.
Use matrices to find out how much cake I eat.
Explore a new way of multiplying with matrices.
Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.
What happens when you find the powers of this matrix?
Explore the shape of a square after it is transformed by the action of a matrix.
Matrices and Complex Numbers combine to enable us to create four dimensional numbers.
Use matrices to model this popular party game.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the properties of matrix transformations with these 10 questions.
Take a look at these recently solved problems.
Try out some calculations. Are you surprised by the results?
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
What is the remainder if you divide a square number by $8$?
Can you show that $n^5-n^3$ is always divisible by $24$?
Can you find the smallest integer which has exactly 426 proper factors?
Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.
If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?
Can you justify this equation involving three angles?
In this short challenge, can you use angle properties in a circle to figure out some trig identities?
Can you find a way to prove the trig identities using a diagram?
Draw graphs of the sine and modulus functions and explain the humps.
Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?
Can you find the sum of the squared sine values?